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Old 2020-09-22, 22:42   #986
sweety439
 
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Nov 2016

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Originally Posted by sweety439 View Post
For R40, these remain k's have algebra factors:

* k=490 (=square*base/4), all odd n are algebraic
* k=11560 (=289*base, 289 itself was eliminated at n=1), all odd n are algebraic
* k=12250 (=square*base/4), all odd n are algebraic
* k=12544 (=square), all even n are algebraic
* k=15376 (=square), all even n are algebraic

For R52, these remain k's have algebra factors:

* k=21316 (=square), all even n are algebraic

For R78, these remain k's have algebra factors:

* k=4489 (=square), all even n are algebraic
* k=7800 (=100*base, 100 itself was eliminated at n=1), all odd n are algebraic
* k=8649 (=square), all even n are algebraic
* k=12167 (=cube), all n divisible by 3 are algebraic
* k=13824 (=cube), all n divisible by 3 are algebraic
* k=59536 (=square), all even n are algebraic

For R96, these remain k's have algebra factors:

* k=1681 (=square), all even n are algebraic
* k=5046 (=square*base/16), all odd n are algebraic
* k=9216 (=1*base^2, 1 itself was eliminated at n=2), all n such that n+2 is not prime are algebraic
* k=16641 (=square), all even n are algebraic

For R106, these remain k's have algebra factors:

* k=64 (=square and cube), all even n and all n divisible by 3 are algebraic
* k=81 (=square), all even n are algebraic
* k=400 (=square), all even n are algebraic
* k=676 (=square), all even n are algebraic
* k=841 (=square), all even n are algebraic
* k=1024 (=square and 5th power), all even n and all n divisible by 5 are algebraic
* k=2116 (=square), all even n are algebraic
* k=3136 (=square), all even n are algebraic
* k=3481 (=square), all even n are algebraic
* k=4096 (=square and cube), all even n and all n divisible by 3 are algebraic
* k=5776 (=square), all even n are algebraic
* k=7744 (=square), all even n are algebraic
* k=10816 (=square), all even n are algebraic
* k=12321 (=square), all even n are algebraic

For R124, these remain k's have algebra factors:

* k=441 (=square), all even n are algebraic
* k=1156 (=square), all even n are algebraic
* k=1519 (=square*base/4), all odd n are algebraic
* k=4096 (=square and cube), all even n and all n divisible by 3 are algebraic
* k=7396 (=square), all even n are algebraic
R88 have more such examples, see post https://mersenneforum.org/showpost.p...&postcount=486
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